Theory
ResearchFrontier structures and internal systems
OverviewSymmetryAsymmetrySet TheoryFormula LabUnified Model

6-32

Diatonic hexachord / Major hexachord

Cardinality
6

Prime Form

Prime form pitch class clockC0C#D2D#E4F5F#G7G#A9A#B[0,2,4,5,7,9]6 pitch classes
T0

Interval Vector

<1,4,3,2,5,0> (sum: 15)
1
ic1
4
ic2
3
ic3
2
ic4
5
ic5
0
ic6
ic1: m2/M7
ic2: M2/m7
ic3: m3/M6
ic4: M3/m6
ic5: P4/P5
ic6: TT
Prime Form
[0,2,4,5,7,9]
Interval Vector
<1,4,3,2,5,0>
T-Symmetry
1
I-Symmetry
1 (inversionally symmetric)
Invariant at I: 9

Step Pattern

2-2-1-2-2-3
Intervals: W-W-H-W-W-3

Complement

6-32card 6
[0,2,4,5,7,9]
Diatonic hexachord

All Transpositions

LevelPitch ClassesNote Names
T0[0,2,4,5,7,9]C D E F G A
T1[1,3,5,6,8,10]C# D# F F# G# A#
T2[2,4,6,7,9,11]D E F# G A B
T3[0,3,5,7,8,10]C D# F G G# A#
T4[1,4,6,8,9,11]C# E F# G# A B
T5[0,2,5,7,9,10]C D F G A A#
T6[1,3,6,8,10,11]C# D# F# G# A# B
T7[0,2,4,7,9,11]C D E G A B
T8[0,1,3,5,8,10]C C# D# F G# A#
T9[1,2,4,6,9,11]C# D E F# A B
T10[0,2,3,5,7,10]C D D# F G A#
T11[1,3,4,6,8,11]C# D# E F# G# B
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